Interplay Between Superconductivity and Charge Order in Near-Critical Metals

非技术总结该奖项支持高温超导子领域凝聚态物理的理论研究和教育。在足够低的温度下，高温超导体变成超导，这是一种电子的协作态，表现出与铜等普通导体截然不同的性质。其中之一是不耗散地传导电力的能力。这项理论研究是由过去几年的实验发现启发的，这些发现表明，超导出现的最高温度往往是其他类型电子态之间边界附近最高的，对于这些电子态，电子自组织起来显示出电子磁性或电子电荷的周期性排列。理解电子之间截然不同的自组织倾向之间的竞争如何增强超导倾向，对于发展对高温超导起源的基本理解是重要的。它还可能有助于发展设计新的超导材料的能力，这些材料在更高的温度下表现出超导电性，并具有使其适合实际应用的特性。该奖项支持详细研究是什么导致电荷和磁序竞争，以及超导如何从这场竞争中获益。这个项目支持在一个活跃的研究领域对研究生和博士后研究人员的专门培训，以及社区对实现高温超导的科学的讨论。技术总结这个项目支持强关联电子系统领域的理论研究和教育。研究集中在两个与量子临界点上的费米子系统的伪隙有关的基本问题上：1.d波超导电性和竞争的非超导秩序之间的竞争；2.当超导电性从量子临界区出现并且正常态与费米液体非常不同时，超导涨落的分析。PI将调查两个相互竞争的序：无公度电荷密度波序和无公度对密度波序。后者可以被认为是具有非零总动量的超导电性。PI和他的研究团队将分析竞争有序的稳定性、有序模式，以及竞争有序的临界波动是否会额外促进超导电性，从而导致转变温度高于相应的量子临界点。在超导波动的分析中，PI和他的团队将详细研究当超导从量子临界区域出现时，超导序参数的纵向波动的影响，在该区域中，配对势与非相干费米子耦合。这项研究的目的是超越传统的Eliashberg型理论，获得完整的Luttinger-Ward泛函，并分析远离极小值的涨落轮廓，检查是否存在一个中间温度范围，在那里已经形成了能隙，但能隙涨落使费米子保持非相干，阻止了真正的超导秩序的发展。在此温度范围内，系统将显示伪隙行为。超导电性和相互竞争的有序之间的相互作用是研究一类奇异超导体的普遍主题，如重费米子、铜酸盐、Ruthenate、铁磷酸盐、有机和分子超导体。在元素超导体中，磁性和超导电性是对立的，但在奇异的超导体中，磁性可能会增强超导的趋势。对量子临界金属的完整相图的分析可能有助于加深对相关电子系统中高温超导所需关键成分的理解。

NONTECHNICAL SUMMARYThis award supports theoretical research and education in condensed matter physics, in the subfield of high temperature superconductivity. At sufficiently low temperature, high temperature superconductors become superconducting, a cooperative state of electrons that exhibits distinctly different properties from those of ordinary conductors like copper. Among them is the ability to conduct electricity without dissipation. This theoretical investigation is inspired by experimental discoveries over the last few years indicating that the highest temperature at which superconductivity appears is often the largest near a boundary between other kinds of electronic states for which the electrons self organize to display periodic arrangements of either electron magnetism or electron charges. The understanding of how the competition among distinctly different tendencies for electrons to self-organize might enhance the tendency for superconductivity is important in developing a fundamental understanding of the origin of high temperature superconductivity. It may also contribute to developing the capability to design new superconducting materials which exhibit superconductivity at higher temperatures and have properties that make them suitable for practical applications. This award supports a detailed study of what causes charge and magnetic orders to compete and how superconductivity gains from this competition. This project supports specialized training of graduate students and postdoctoral researchers in an active area of research, as well as community discussions of the science that enables high temperature superconductivity.TECHNICAL SUMMARYThis project supports theoretical research and education in the field of strongly correlated electron systems. The research is focused on two fundamental issues related to the pseudo gap in systems of fermions tuned to a quantum-critical point: 1. the competition between d-wave superconductivity and competing non-superconducting orders, and 2. the analysis of superconducting fluctuations when superconductivity emerges from a quantum-critical regime and the normal state is very different from that of a Fermi liquid. The PI will investigate two competing orders: incommensurate charge density wave order and incommensurate pair density wave order. The latter can be considered as superconductivity with a non-zero total momentum of a pair. The PI and his research team will analyze the stability of competing orders, ordering patterns, and whether critical fluctuations of competing orders give an additional boost to superconductivity leading to transition temperatures above the corresponding quantum-critical points. In the analysis of superconducting fluctuations, the PI and his team will study in detail the effects of longitudinal fluctuations of a superconducting order parameter in a situation when superconductivity emerges from a quantum-critical regime in which a pairing potential couples incoherent fermions. The goal of this study is to go beyond conventional Eliashberg-type theories to obtain the full Luttinger-Ward functional, and analyze the profile of fluctuations away from the minimum and check the existence of an intermediate temperature range where the gap is already developed, but gap fluctuations keep fermions incoherent and prevent a true superconducting order to develop. In this temperature range the system will display the pseudogap behavior. The interplay between superconductivity and competing orders is a pervasive theme in the study of classes of exotic superconductors, such as the heavy fermion, cuprate, ruthenate, Fe-pnictide, organic and molecular superconductors. Magnetism and superconductivity are antithetical in elemental superconductors, but in exotic superconductors magnetism may enhance the tendency toward superconductivity. The analysis of the full phase diagram of quantum-critical metals may help advance understanding of the key ingredients required for high- temperature superconductivity in correlated electron systems.